Highest Common Factor of 715, 8702 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 715, 8702 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 715, 8702 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 715, 8702 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 715, 8702 is 1.
HCF(715, 8702) = 1
HCF of 715, 8702 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 715, 8702 is 1.
Highest Common Factor of 715,8702 is 1
Step 1: Since 8702 > 715, we apply the division lemma to 8702 and 715, to get
8702 = 715 x 12 + 122
Step 2: Since the reminder 715 ≠ 0, we apply division lemma to 122 and 715, to get
715 = 122 x 5 + 105
Step 3: We consider the new divisor 122 and the new remainder 105, and apply the division lemma to get
122 = 105 x 1 + 17
We consider the new divisor 105 and the new remainder 17,and apply the division lemma to get
105 = 17 x 6 + 3
We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get
17 = 3 x 5 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 715 and 8702 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(105,17) = HCF(122,105) = HCF(715,122) = HCF(8702,715) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 715, 8702 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 715, 8702?
Answer: HCF of 715, 8702 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 715, 8702 using Euclid's Algorithm?
Answer: For arbitrary numbers 715, 8702 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.